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arXiv · 2004.05492

Integrality of twisted L-values of elliptic curves

Hanneke Wiersema·Christian Wuthrich
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Abstract

Under suitable, fairly weak hypotheses on an elliptic curve $E/\mathbb{Q}$ and a primitive non-trivial Dirichlet character $\chi$, we show that the algebraic $L$-value $\mathscr{L}(E,\chi)$ at $s=1$ is an algebraic integer. For instance, for semistable curves $\mathscr{L}(E,\chi)$ is integral whenever $E$ admits no isogenies defined over $\mathbb{Q}$. Moreover we give examples illustrating that our hypotheses are necessary for integrality to hold.

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Hanneke Wiersema, Christian Wuthrich. 2020-04-11. Integrality of twisted L-values of elliptic curves. https://arxiv.org/abs/2004.05492

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